Seismic risk analysis for structural engineering purposes is primarily based on peak ground accelerations taken from earthquake records. The study investigates the use of simple, non stationary ARMA models to represent underlying earthquake events. Measured earthquake records are considered to be random samples. Models are developed and samples of acceleration records are generated for 4 major events. Maximum displacement ductility demand, normalized hysteretic energy demand and a simple damage index spectra for bi-linear and stiffness softening SDOF systems are computed for these samples of accelerograms. The sensitivity of demand spectra to ARMA model characteristics are also examined. It is concluded that, for the events studied, simple ARMA models may be considered to capture most of the information contained in earthquake acceleration records insofar as non linear response spectra are concerned. It was found that, for each event, the average of the logarithms of displacement ductility and hysteretic energy demand for bi-linear systems are very nearly linearly related to the logarithms of system period for SDOF systems.